强Ockham代数与剩余格  

Strong Ockham algebra and residuated lattice

作　　者：张隆传[1] 张小红[1] 

机构地区：[1]宁波大学数学系,浙江宁波315211

出　　处：《纯粹数学与应用数学》2010年第1期123-130,145,共9页Pure and Applied Mathematics

基　　金：国家自然科学基金(60775038);宁波市自然科学基金(2009A610078);宁波大学王宽诚幸福基金

摘　　要：首先讨论了Ockham代数与剩余格的关系,引入了强Ockham代数的概念,并讨论了它的基本性质.然后,将著名的R_0蕴涵和R_0算子推广到Ockham代数上,证明了添加广义R_0蕴涵和广义R_0算子后的Ockham代数L成为剩余格的充要条件是L为强Ockham代数.最后给出若干重要例子,以此来说明强Ockham代数的条件是独立的.Firstly, the relation between Ockham algebras and residuated lattice are investigated, and the notion of Strong Ockham algebras is introduced, and its elementary properties are given. Secondly, the famous Ro implication and Ro operator are developed to Ockham algebras, which are called general Ro implication and general R0 operator. And the necessary and sufficient condition is proved as following： a Ockham algebra L with general Ro implication and general Ro operator becomes a Residuated lattice if and only if L is a Strong Ockham algebras. Finally, Some important examples are given to show that three conditions of Strong Ockham algebras are independent.

关 键 词：模糊逻辑 强De MORGAN代数 OCKHAM代数 剩余格 强Ockham代数 

分 类 号：O153.1[理学—数学]